An evaluation of length-frequency sampling procedures and subsequent data analysis for purse seine-caught yellowfin tuna in the Eastern Pacific Ocean

ENGLISH: A two-stage sampling design is used to estimate the variances of the numbers of yellowfin in different age groups caught in the eastern Pacific Ocean. For purse seiners, the primary sampling unit (n) is a brine well containing fish from a month-area stratum; the number of fish lengths (m) measured from each well are the secondary units. The fish cannot be selected at random from the wells because of practical limitations. The effects of different sampling methods and other factors on the reliability and precision of statistics derived from the length-frequency data were therefore examined. Modifications are recommended where necessary. Lengths of fish measured during the unloading of six test wells revealed two forms of inherent size stratification: 1) short-term disruptions of existing pattern of sizes, and 2) transition zones between long-term trends in sizes. To some degree, all wells exhibited cyclic changes in mean size and variance during unloading. In half of the wells, it was observed that size selection by the unloaders induced a change in mean size. As a result of stratification, the sequence of sizes removed from all wells was non-random, regardless of whether a well contained fish from a single set or from more than one set. The number of modal sizes in a well was not related to the number of sets. In an additional well composed of fish from several sets, an experiment on vertical mixing indicated that a representative sample of the contents may be restricted to the bottom half of the well. The contents of the test wells were used to generate 25 simulated wells and to compare the results of three sampling methods applied to them. The methods were: (1) random sampling (also used as a standard), (2) protracted sampling, in which the selection process was extended over a large portion of a well, and (3) measuring fish consecutively during removal from the well. Repeated sampling by each method and different combinations indicated that, because the principal source of size variation occurred among primary units, increasing n was the most effective way to reduce the variance estimates of both the age-group sizes and the total number of fish in the landings. Protracted sampling largely circumvented the effects of size stratification, and its performance was essentially comparable to that of random sampling. Sampling by this method is recommended. Consecutive-fish sampling produced more biased estimates with greater variances. Analysis of the 1988 length-frequency samples indicated that, for age groups that appear most frequently in the catch, a minimum sampling frequency of one primary unit in six for each month-area stratum would reduce the coefficients of variation (CV) of their size estimates to approximately 10 percent or less. Additional stratification of samples by set type, rather than month-area alone, further reduced the CV's of scarce age groups, such as the recruits, and potentially improved their accuracy. The CV's of recruitment estimates for completely-fished cohorts during the 198184 period were in the vicinity of 3 to 8 percent. Recruitment estimates and their variances were also relatively insensitive to changes in the individual quarterly catches and variances, respectively, of which they were composed. SPANISH: Se usa un diseño de muestreo de dos etapas para estimar las varianzas de los números de aletas amari11as en distintos grupos de edad capturados en el Océano Pacifico oriental. Para barcos cerqueros, la unidad primaria de muestreo (n) es una bodega de salmuera que contenía peces de un estrato de mes-área; el numero de ta11as de peces (m) medidas de cada bodega es la unidad secundaria. Limitaciones de carácter practico impiden la selección aleatoria de peces de las bodegas. Por 10 tanto, fueron examinados los efectos de distintos métodos de muestreo y otros factores sobre la confiabilidad y precisión de las estadísticas derivadas de los datos de frecuencia de ta11a. Se recomiendan modificaciones donde sean necesarias. Las ta11as de peces medidas durante la descarga de seis bodegas de prueba revelaron dos formas de estratificación inherente por ta11a: 1) perturbaciones a corto plazo en la pauta de ta11as existente, y 2) zonas de transición entre las tendencias a largo plazo en las ta11as. En cierto grado, todas las bodegas mostraron cambios cíclicos en ta11a media y varianza durante la descarga. En la mitad de las bodegas, se observo que selección por ta11a por los descargadores indujo un cambio en la ta11a media. Como resultado de la estratificación, la secuencia de ta11as sacadas de todas las bodegas no fue aleatoria, sin considerar si una bodega contenía peces de un solo lance 0 de mas de uno. El numero de ta11as modales en una bodega no estaba relacionado al numero de lances. En una bodega adicional compuesta de peces de varios lances, un experimento de mezcla vertical indico que una muestra representativa del contenido podría estar limitada a la mitad inferior de la bodega. Se uso el contenido de las bodegas de prueba para generar 25 bodegas simuladas y comparar los resultados de tres métodos de muestreo aplicados a estas. Los métodos fueron: (1) muestreo aleatorio (usado también como norma), (2) muestreo extendido, en el cual el proceso de selección fue extendido sobre una porción grande de una bodega, y (3) medición consecutiva de peces durante la descarga de la bodega. EI muestreo repetido con cada método y distintas combinaciones de n y m indico que, puesto que la fuente principal de variación de ta11a ocurría entre las unidades primarias, aumentar n fue la manera mas eficaz de reducir las estimaciones de la varianza de las ta11as de los grupos de edad y el numero total de peces en los desembarcos. El muestreo extendido evito mayormente los efectos de la estratificación por ta11a, y su desempeño fue esencialmente comparable a aquel del muestreo aleatorio. Se recomienda muestrear con este método. El muestreo de peces consecutivos produjo estimaciones mas sesgadas con mayores varianzas. Un análisis de las muestras de frecuencia de ta11a de 1988 indico que, para los grupos de edad que aparecen con mayor frecuencia en la captura, una frecuencia de muestreo minima de una unidad primaria de cada seis para cada estrato de mes-área reduciría los coeficientes de variación (CV) de las estimaciones de ta11a correspondientes a aproximadamente 10% 0 menos. Una estratificación adicional de las muestras por tipo de lance, y no solamente mes-área, redujo aun mas los CV de los grupos de edad escasos, tales como los reclutas, y mejoró potencialmente su precisión. Los CV de las estimaciones del reclutamiento para las cohortes completamente pescadas durante 1981-1984 fueron alrededor de 3-8%. Las estimaciones del reclutamiento y sus varianzas fueron también relativamente insensibles a cambios en las capturas de trimestres individuales y las varianzas, respectivamente, de las cuales fueron derivadas. (PDF contains 70 pages)

Wadge Bank trawl fishery studies. Pt. 4. An analysis of the length frequency measurements of the sea bream (Lethrinus nebulosus) made in 1949 and 1953 to 1958

Length frequency distributions of the sea bream collected during the period 1953 to 1958 have been analysed. The increase in average sizes of the sea bream with depth suggests a movement to deeper waters with increase in size. By numbers, the sea bream is more abundant between 21 and 30 fathoms than in deeper areas. The recruitment was continuous and regular. There is no sign of entry or progression of a dominant brood throughout the period under study. Length frequency distribution shows three distinct modes. The first mode occurs regularly but does not progress beyond 40cm, recruitment being balanced by natural and fishing mortality. The other two which are not regular are probably the result of fishing outside regular areas. Short sections of “growth” lines which fit into one another when extrapolated, are evident. The larger lines obtained by extrapolation are parallel to one another. These tentative "growth lines" indicate that this species which enters the fishing grounds, when 15 cm or larger in length are exploited by the trawl fishery for a period of three to four years. This species appears to be six months old when it enters the fishing grounds and increases in length by about 37.5 cm in the next 30 months. Later growth slows down. The average size of the specimens sampled continued to get smaller from 1953 till 1957. It is shown that this reduction in size is due to increased fishing effort.

Improving Shepherd's Length Composition Analysis (SLCA) method for growth parameter estimations

Shepherd's "weekly parametric" method for estimating the parameter L sub( infinity ) and K of the von Bertalanffy growth function from length-frequency data often fails to converge, and usually overestimates K. It is shown that this is due to overcounting of the frequencies associated with large, slow growing fish, and that both of these problems can be completely overcome by a simple change in the way the scoring function is formulated.

Length-frequency estimation for yellowfin tuna (Thunnus albacares) caught by commercial fishing gear in the Eastern Pacific Ocean

ENGLISH: Methods of collecting samples for the purpose of estimating the numbers and weights of fish caught, by length interval, are described. Several models for two-stage sampling are described, and the equations for the estimators and their variances are given. The results from a brief simulation study are used to show the differences between estimates made with the different models. Estimators for the average weights of fish in the catch and their variances are also described. These average weights are used to provide improved estimates of the total annual catches of yellowfin taken from the eastern Pacific Ocean, east of 150°W, between 1955 and 1990. SPANISH: Se describen los métodos de recoger de muestreo para estimar el número o peso de peces capturados, por intervalo de talla. Se describen varios modelos para el muestreo de dos etapas, y se presentan las ecuaciones para los estimadores y sus varianzas. Se usan los resultados de un breve estudio de simulación para indicar las diferencias entre estimaciones realizadas con los distintosmodelos. También se describe un estimador para el peso promedio de peces en la captura y su varianza. Se usan estos estimadores para calcular estimaciones mejoradas de las capturas anuales totales de aleta amarilla tomadas del Océano Pacífico oriental, al este de 150°W, entre 1955 y 1990. (PDF contains 41 pages.)

Growth and age composition of northern bluefin tuna, Thunnus thynnus, caught in the Eastern Pacific Ocean, as estimated from length-frequency data, with comments on trans-Pacific migrations

ENGLISH: The spawning of Pacific northern bluefin tuna, Thunnus thynnus, takes place only in the western Pacific Ocean (WPO), but substantial numbers of the juveniles migrate to the eastern Pacific Ocean (EPO), where they remain for several months, or longer, and the.n return to the WPO. Lengthfrequency and tagging data show that many bluefin arrive in the EPO as 1-and 2-year olds, and remain there for one or two fishing seasons before returning to the WPO. The proportion of the fish which make the west-to-east migration varies among years. The numbers of 1-, 2-, 3-, 4, and >4 –year olds in the catches of the EPO are estimated for most years of the 1952-1991 period. SPANISH: EI desove del atun aleta azul del norte del Pacifico, Thunnus thynnus, ocurre solamente en el Océano Pacifico occidental (WPO), pero números substanciales de los juveniles migran al Océano Pacifico oriental (OPO), donde permanecen unos meses, 0 mas, antes de regresar al WPO. Datos de marcado y frecuencia de talla indican que muchos aletas azules llegan al OPO a 1 o 2 anos de edad, y permanecen alIi una 0 dos temporadas de pesca antes de regresar al WPO. La proporcion de los peces que migra del oeste al este varia entre anos. Se estima el numero de peces de 1, 2, 3, 4, Y>4 anos de edad en las capturas del OPO para la mayoria de los anos del periodo de 1952-1991. (PDF contains 40 pages.)

Precision estimates and suggested sample sizes for length-frequency data

For most fisheries applications, the shape of a length-frequency distribution is much more important than its mean length or variance. This makes it difficult to evaluate at which point a sample size is adequate. By estimating the coefficient of variation of the counts in each length class and taking a weighted mean of these, a measure of precision was obtained that takes the precision in all length classes into account. The precision estimates were closely associated with the ratio of the sample size to the number of size classes in each sample. As a rule-of-thumb, a minimum sample size of 10 times the number of length classes in the sample is suggested because the precision deteriorates rapidly for smaller sample sizes. In absence of such a rule-of-thumb, samplers have previously under-estimated the required sample size for samples with large fish, while over-sampling small fish of the same species.

Evaluating mortality using length-frequency data when growth parameters are poorly known

A method is presented through which the total mortality undergone by several fish stocks of the same species can be compared when growth parameters are poorly known or unknown. Whereas the estimate of Z obtained via the length-converted catch curve is highly sensitive to the input parameters K and L sub( infinity ), the ratio of Z estimates obtained for different stocks with the same combination of parameters is almost independent of these inputs, at least when the fit of the linear regression is good. The method is tested on simulated data and an application is presented using real data from the Lesser Antilles. It provides the possibility of qualitatively comparing several stocks in situations of scarce biological knowledge.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Drought frequency analysis for California from observed, synthetic, and proxy data

Drought frequency analysis can be performed with statistical techniques developed for determining recurrence intervals for extreme precipitation and flood events (Linsley et al 1992). The drought analysis method discussed in this paper uses the log-Pearson Type III distribution, which has been widely used in flood frequency research. Some of the difficulties encountered when using this distribution for drought analysis are investigated.

Length frequency and growth studies on Cynoglossus macrolepidotus (Bleeker) off Bombay coast

Specimens randomly collected from Sassoon Docks, Bombay, India, at monthly intervals during 1979 to 1981 were considered for age/growth studies. Cynoglossus macrolepidotus, the fish, attained a length of 202 mm at 1 year, 250 mm at 1 1/2 year and 272 mm at 21 months respectively; the maximum length of the fish could be 353 mm and the life span could be 7 years. The scale ring studies showed presence of only 0 to 3+ rings. Majority of the fishes were of 1 and 1+ year class.